Answer:
In first picture,
m∠C = m∠B
⇒ AC = AB
⇒ x + 9 = 2x - 8
⇒ x - 2x = -8 - 9
⇒ -x = -17
⇒ x = 17
Hence, the length of BC = x = 17 units,
In second picture,
m∠A = m∠B = m∠C
⇒ Triangle ABC is an equilateral triangle,
⇒ AB = BC = CA
⇒ 4x - 10 = 5x - 22 = 3x + 2
When,
⇒ 4x - 10 = 5x - 22
⇒ 4x - 5x = -22 + 10
⇒ -x = -12
⇒ x = 12
Hence, the value of x is 12.
In third picture,
LN = LM = NM
The triangle LMN is an equilateral triangle,
⇒ m∠L = m∠M = m∠N = 60°
⇒ m∠L= 60°
⇒ 7x - 3 = 60
⇒ 7x = 63
⇒ x = 9
Hence, the value of x is 9.
